Cortical patterns and gamma genesis are modulated by reversal potentials and gap-junction diffusion

  • M.L. Steyn-Ross
  • D.A. Steyn-Ross
  • M.T. Wilson
  • J.W. Sleigh
Part of the Springer Series in Computational Neuroscience book series (NEUROSCI, volume 4)


In this chapter we describe a continuum model for the cortex that includes both axon-to-dendrite chemical synapses and direct neuron-to-neuron gap-junction diffusive synapses. The effectiveness of chemical synapses is determined by the voltage of the receiving dendrite V relative to its Nernst reversal potential \(V^{\rm rev}{}\). Here we explore two alternative strategies for incorporating dendritic reversal potentials, and uncover surprising differences in their stability properties and model dynamics. In the “slow-soma” variant, the \((V^{\rm rev} - V)\) weighting is applied after the input flux has been integrated at the dendrite, while for “fast-soma”, the weighting is applied directly to the input flux, prior to dendritic integration. For the slow-soma case, we find that–-provided the inhibitory diffusion (via gap-junctions) is sufficiently strong–-the cortex generates stationary Turing patterns of cortical activity. In contrast, the fast-soma destabilizes in favor of standing-wave spatial structures that oscillate at low-gamma frequency (\(\sim\)30-Hz); these spatial patterns broaden and weaken as diffusive coupling increases, and disappear altogether at moderate levels of diffusion. We speculate that the slow- and fast-soma models might correspond respectively to the idling and active modes of the cortex, with slow-soma patterns providing the default background state, and emergence of gamma oscillations in the fast-soma case signaling the transition into the cognitive state.

gap junctions cortical patterns gamma oscillation bifurcation Turing instability wave instability 



We thank Chris Rennie for helpful discussions on convolution formulations for the cortex. This research was supported by the Royal Society of New Zealand Marsden Fund, contract 07-UOW-037.


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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • M.L. Steyn-Ross
    • 1
  • D.A. Steyn-Ross
    • 2
  • M.T. Wilson
    • 2
  • J.W. Sleigh
    • 2
  1. 1.Department of EngineeringUniversity of WaikatoHamiltonNew Zealand
  2. 2.Waikato Clinical SchoolUniversity of Auckland, Waikato HospitalHamiltonNew Zealand

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